/**********************************************************************
- * Copyright (c) 2013, 2014 Pieter Wuille *
+ * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
-#ifndef _SECP256K1_ECMULT_GEN_IMPL_H_
-#define _SECP256K1_ECMULT_GEN_IMPL_H_
+#ifndef SECP256K1_ECMULT_GEN_IMPL_H
+#define SECP256K1_ECMULT_GEN_IMPL_H
+#include "util.h"
#include "scalar.h"
#include "group.h"
#include "ecmult_gen.h"
+#include "hash_impl.h"
+#ifdef USE_ECMULT_STATIC_PRECOMPUTATION
+#include "ecmult_static_context.h"
+#endif
-typedef struct {
- /* For accelerating the computation of a*G:
- * To harden against timing attacks, use the following mechanism:
- * * Break up the multiplicand into groups of 4 bits, called n_0, n_1, n_2, ..., n_63.
- * * Compute sum(n_i * 16^i * G + U_i, i=0..63), where:
- * * U_i = U * 2^i (for i=0..62)
- * * U_i = U * (1-2^63) (for i=63)
- * where U is a point with no known corresponding scalar. Note that sum(U_i, i=0..63) = 0.
- * For each i, and each of the 16 possible values of n_i, (n_i * 16^i * G + U_i) is
- * precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0..63).
- * None of the resulting prec group elements have a known scalar, and neither do any of
- * the intermediate sums while computing a*G.
- */
- secp256k1_fe_t prec[64][16][2]; /* prec[j][i] = (16^j * i * G + U_i).{x,y} */
-} secp256k1_ecmult_gen_consts_t;
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+ static const size_t SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE = ROUND_TO_ALIGN(sizeof(*((secp256k1_ecmult_gen_context*) NULL)->prec));
+#else
+ static const size_t SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE = 0;
+#endif
-static const secp256k1_ecmult_gen_consts_t *secp256k1_ecmult_gen_consts = NULL;
+static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context *ctx) {
+ ctx->prec = NULL;
+}
-static void secp256k1_ecmult_gen_start(void) {
- if (secp256k1_ecmult_gen_consts != NULL)
- return;
+static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx, void **prealloc) {
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+ secp256k1_ge prec[ECMULT_GEN_PREC_N * ECMULT_GEN_PREC_G];
+ secp256k1_gej gj;
+ secp256k1_gej nums_gej;
+ int i, j;
+ size_t const prealloc_size = SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE;
+ void* const base = *prealloc;
+#endif
- /* Allocate the precomputation table. */
- secp256k1_ecmult_gen_consts_t *ret = (secp256k1_ecmult_gen_consts_t*)checked_malloc(sizeof(secp256k1_ecmult_gen_consts_t));
+ if (ctx->prec != NULL) {
+ return;
+ }
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+ ctx->prec = (secp256k1_ge_storage (*)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G])manual_alloc(prealloc, prealloc_size, base, prealloc_size);
/* get the generator */
- const secp256k1_ge_t *g = &secp256k1_ge_consts->g;
- secp256k1_gej_t gj; secp256k1_gej_set_ge(&gj, g);
+ secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
/* Construct a group element with no known corresponding scalar (nothing up my sleeve). */
- secp256k1_gej_t nums_gej;
{
- static const unsigned char nums_b32[32] = "The scalar for this x is unknown";
- secp256k1_fe_t nums_x;
- VERIFY_CHECK(secp256k1_fe_set_b32(&nums_x, nums_b32));
- secp256k1_ge_t nums_ge;
- VERIFY_CHECK(secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0));
+ static const unsigned char nums_b32[33] = "The scalar for this x is unknown";
+ secp256k1_fe nums_x;
+ secp256k1_ge nums_ge;
+ int r;
+ r = secp256k1_fe_set_b32(&nums_x, nums_b32);
+ (void)r;
+ VERIFY_CHECK(r);
+ r = secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0);
+ (void)r;
+ VERIFY_CHECK(r);
secp256k1_gej_set_ge(&nums_gej, &nums_ge);
/* Add G to make the bits in x uniformly distributed. */
- secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, g);
+ secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, &secp256k1_ge_const_g, NULL);
}
/* compute prec. */
- secp256k1_ge_t prec[1024];
{
- secp256k1_gej_t precj[1024]; /* Jacobian versions of prec. */
- secp256k1_gej_t gbase; gbase = gj; /* 16^j * G */
- secp256k1_gej_t numsbase; numsbase = nums_gej; /* 2^j * nums. */
- for (int j=0; j<64; j++) {
- /* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */
- precj[j*16] = numsbase;
- for (int i=1; i<16; i++) {
- secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase);
+ secp256k1_gej precj[ECMULT_GEN_PREC_N * ECMULT_GEN_PREC_G]; /* Jacobian versions of prec. */
+ secp256k1_gej gbase;
+ secp256k1_gej numsbase;
+ gbase = gj; /* PREC_G^j * G */
+ numsbase = nums_gej; /* 2^j * nums. */
+ for (j = 0; j < ECMULT_GEN_PREC_N; j++) {
+ /* Set precj[j*PREC_G .. j*PREC_G+(PREC_G-1)] to (numsbase, numsbase + gbase, ..., numsbase + (PREC_G-1)*gbase). */
+ precj[j*ECMULT_GEN_PREC_G] = numsbase;
+ for (i = 1; i < ECMULT_GEN_PREC_G; i++) {
+ secp256k1_gej_add_var(&precj[j*ECMULT_GEN_PREC_G + i], &precj[j*ECMULT_GEN_PREC_G + i - 1], &gbase, NULL);
}
- /* Multiply gbase by 16. */
- for (int i=0; i<4; i++) {
- secp256k1_gej_double_var(&gbase, &gbase);
+ /* Multiply gbase by PREC_G. */
+ for (i = 0; i < ECMULT_GEN_PREC_B; i++) {
+ secp256k1_gej_double_var(&gbase, &gbase, NULL);
}
/* Multiply numbase by 2. */
- secp256k1_gej_double_var(&numsbase, &numsbase);
- if (j == 62) {
+ secp256k1_gej_double_var(&numsbase, &numsbase, NULL);
+ if (j == ECMULT_GEN_PREC_N - 2) {
/* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
secp256k1_gej_neg(&numsbase, &numsbase);
- secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej);
+ secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL);
}
}
- secp256k1_ge_set_all_gej_var(1024, prec, precj);
+ secp256k1_ge_set_all_gej_var(prec, precj, ECMULT_GEN_PREC_N * ECMULT_GEN_PREC_G);
}
- for (int j=0; j<64; j++) {
- for (int i=0; i<16; i++) {
- VERIFY_CHECK(!secp256k1_ge_is_infinity(&prec[j*16 + i]));
- ret->prec[j][i][0] = prec[j*16 + i].x;
- ret->prec[j][i][1] = prec[j*16 + i].y;
+ for (j = 0; j < ECMULT_GEN_PREC_N; j++) {
+ for (i = 0; i < ECMULT_GEN_PREC_G; i++) {
+ secp256k1_ge_to_storage(&(*ctx->prec)[j][i], &prec[j*ECMULT_GEN_PREC_G + i]);
}
}
+#else
+ (void)prealloc;
+ ctx->prec = (secp256k1_ge_storage (*)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G])secp256k1_ecmult_static_context;
+#endif
+ secp256k1_ecmult_gen_blind(ctx, NULL);
+}
- /* Set the global pointer to the precomputation table. */
- secp256k1_ecmult_gen_consts = ret;
+static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx) {
+ return ctx->prec != NULL;
}
-static void secp256k1_ecmult_gen_stop(void) {
- if (secp256k1_ecmult_gen_consts == NULL)
- return;
+static void secp256k1_ecmult_gen_context_finalize_memcpy(secp256k1_ecmult_gen_context *dst, const secp256k1_ecmult_gen_context *src) {
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+ if (src->prec != NULL) {
+ /* We cast to void* first to suppress a -Wcast-align warning. */
+ dst->prec = (secp256k1_ge_storage (*)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G])(void*)((unsigned char*)dst + ((unsigned char*)src->prec - (unsigned char*)src));
+ }
+#else
+ (void)dst, (void)src;
+#endif
+}
- secp256k1_ecmult_gen_consts_t *c = (secp256k1_ecmult_gen_consts_t*)secp256k1_ecmult_gen_consts;
- secp256k1_ecmult_gen_consts = NULL;
- free(c);
+static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context *ctx) {
+ secp256k1_scalar_clear(&ctx->blind);
+ secp256k1_gej_clear(&ctx->initial);
+ ctx->prec = NULL;
}
-static void secp256k1_ecmult_gen(secp256k1_gej_t *r, const secp256k1_scalar_t *gn) {
- const secp256k1_ecmult_gen_consts_t *c = secp256k1_ecmult_gen_consts;
- secp256k1_gej_set_infinity(r);
- secp256k1_ge_t add;
- add.infinity = 0;
+static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp256k1_gej *r, const secp256k1_scalar *gn) {
+ secp256k1_ge add;
+ secp256k1_ge_storage adds;
+ secp256k1_scalar gnb;
int bits;
- for (int j=0; j<64; j++) {
- bits = secp256k1_scalar_get_bits(gn, j * 4, 4);
- for (int i=0; i<16; i++) {
- secp256k1_fe_cmov(&add.x, &c->prec[j][i][0], i == bits);
- secp256k1_fe_cmov(&add.y, &c->prec[j][i][1], i == bits);
+ int i, j;
+ memset(&adds, 0, sizeof(adds));
+ *r = ctx->initial;
+ /* Blind scalar/point multiplication by computing (n-b)G + bG instead of nG. */
+ secp256k1_scalar_add(&gnb, gn, &ctx->blind);
+ add.infinity = 0;
+ for (j = 0; j < ECMULT_GEN_PREC_N; j++) {
+ bits = secp256k1_scalar_get_bits(&gnb, j * ECMULT_GEN_PREC_B, ECMULT_GEN_PREC_B);
+ for (i = 0; i < ECMULT_GEN_PREC_G; i++) {
+ /** This uses a conditional move to avoid any secret data in array indexes.
+ * _Any_ use of secret indexes has been demonstrated to result in timing
+ * sidechannels, even when the cache-line access patterns are uniform.
+ * See also:
+ * "A word of warning", CHES 2013 Rump Session, by Daniel J. Bernstein and Peter Schwabe
+ * (https://cryptojedi.org/peter/data/chesrump-20130822.pdf) and
+ * "Cache Attacks and Countermeasures: the Case of AES", RSA 2006,
+ * by Dag Arne Osvik, Adi Shamir, and Eran Tromer
+ * (http://www.tau.ac.il/~tromer/papers/cache.pdf)
+ */
+ secp256k1_ge_storage_cmov(&adds, &(*ctx->prec)[j][i], i == bits);
}
+ secp256k1_ge_from_storage(&add, &adds);
secp256k1_gej_add_ge(r, r, &add);
}
bits = 0;
secp256k1_ge_clear(&add);
+ secp256k1_scalar_clear(&gnb);
}
-#endif
+/* Setup blinding values for secp256k1_ecmult_gen. */
+static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32) {
+ secp256k1_scalar b;
+ secp256k1_gej gb;
+ secp256k1_fe s;
+ unsigned char nonce32[32];
+ secp256k1_rfc6979_hmac_sha256 rng;
+ int overflow;
+ unsigned char keydata[64] = {0};
+ if (seed32 == NULL) {
+ /* When seed is NULL, reset the initial point and blinding value. */
+ secp256k1_gej_set_ge(&ctx->initial, &secp256k1_ge_const_g);
+ secp256k1_gej_neg(&ctx->initial, &ctx->initial);
+ secp256k1_scalar_set_int(&ctx->blind, 1);
+ }
+ /* The prior blinding value (if not reset) is chained forward by including it in the hash. */
+ secp256k1_scalar_get_b32(nonce32, &ctx->blind);
+ /** Using a CSPRNG allows a failure free interface, avoids needing large amounts of random data,
+ * and guards against weak or adversarial seeds. This is a simpler and safer interface than
+ * asking the caller for blinding values directly and expecting them to retry on failure.
+ */
+ memcpy(keydata, nonce32, 32);
+ if (seed32 != NULL) {
+ memcpy(keydata + 32, seed32, 32);
+ }
+ secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, seed32 ? 64 : 32);
+ memset(keydata, 0, sizeof(keydata));
+ /* Accept unobservably small non-uniformity. */
+ secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
+ overflow = !secp256k1_fe_set_b32(&s, nonce32);
+ overflow |= secp256k1_fe_is_zero(&s);
+ secp256k1_fe_cmov(&s, &secp256k1_fe_one, overflow);
+ /* Randomize the projection to defend against multiplier sidechannels. */
+ secp256k1_gej_rescale(&ctx->initial, &s);
+ secp256k1_fe_clear(&s);
+ secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
+ secp256k1_scalar_set_b32(&b, nonce32, NULL);
+ /* A blinding value of 0 works, but would undermine the projection hardening. */
+ secp256k1_scalar_cmov(&b, &secp256k1_scalar_one, secp256k1_scalar_is_zero(&b));
+ secp256k1_rfc6979_hmac_sha256_finalize(&rng);
+ memset(nonce32, 0, 32);
+ secp256k1_ecmult_gen(ctx, &gb, &b);
+ secp256k1_scalar_negate(&b, &b);
+ ctx->blind = b;
+ ctx->initial = gb;
+ secp256k1_scalar_clear(&b);
+ secp256k1_gej_clear(&gb);
+}
+
+#endif /* SECP256K1_ECMULT_GEN_IMPL_H */
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